Question

Sub 24
Ques. 29

The mass of a metal cylinder varies jointly as its height and the square of the radius of its base. One cylinder has a mass of 120 g. Find the mass of a second cylinder made of the same metal, 3 times as high, and having one-half the base radius of the first.

Answer 1

The mass of a metal cylinder varies jointly as its height and the square of the radius of its base. One cylinder has a mass of $120\,\mathrm{g}$. Find the mass of a second cylinder made of the same metal, 3 times as high, and having one-half the base radius of the first.

Solution

$$\begin{array}{l} m = \rho V = \rho h S = \rho h \pi r^{2} \gg \frac{m_{2}}{m_{1}} = \frac{h_{2} r_{2}^{2}}{h_{1} r_{1}^{2}} = 3 * \left(\frac{1}{2}\right)^{2} = \frac{3}{4} \gg m_{2} = \frac{3}{4} * 120\,\mathrm{g} \\ = 90\,\mathrm{g} \end{array}$$